A model for shear behavior of anchors in external shear

A model for shear behavior of anchors in external shear walled frames

İffet Feyza Çırak*1, Hasan Kaplan2, Salih Yılmaz3, Özlem Çalışkan

Değirmenci4, Nihat Çetinkaya2

Online Publication Date: 4 May 2015

URL: http://www.jresm.org/archive/resm2015.05st0211.html

DOI: http://dx.doi.org/10.17515/resm2015.05st0211

Journal Abbreviation: Res. Eng. Struct. Mat.

To cite this article

Çırak İF, Kaplan H, Yılmaz S, Değirmenci ÖÇ, Çetinkaya N. A model for shear behavior of

anchors in external shear walled frames. Res. Eng. Struct. Mat., 2015; 1: 53– 71.

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http://www.jresm.org/archive/resm2015.05st0211.html

http://dx.doi.org/10.17515/resm2015.05st0211

*Corresponding author: [email protected] DOI: http://dx.doi.org/10.17515/resm2015.05st0211

Res. Eng. Struct. Mat. Vol.1 Iss.2 (2015) 53 – 71 53

Research Article

A model for shear behavior of anchors in external shear walled frames

İffet Feyza Çırak*1, Hasan Kaplan2, Salih Yılmaz3, Özlem Çalışkan Değirmenci4, Nihat Çetinkaya2

1Suleyman Demirel University, Department of Civil Engineering, Turkey 2 Pamukkale University, Department of Civil Engineering, Turkey 3 Kâtip Çelebi University, Department of Civil Engineering, Turkey 4Bilecik Şeyh Edebali University, Department of Civil Engineering, Turkey

Article Info Abstract

Article history: Received 11 Feb 2015 Revised 14 Apr 2015 Accepted 15 Apr 2015

Retrofit of the existing seismically deficient buildings is a common need especially in earthquake prone regions. Chemical anchors are widely used to connect existing and newly added structural elements, such as shear walls. Therefore, modelling the behaviour of anchors which transfer axial and shear forces to the added members is important for design and analyses. There is no anchor model present in the current literature accounting shear behaviour. Therefore, a new model is established using results of a comprehensive experimental study conducted at Pamukkale University Earthquake and Construction Technology Research Laboratory. In this study, mentioned shear model is tested using two- story, one-bay RC frame specimens strengthened with external shear walls. In analyses of the models, SAP 2000 software is used and nonlinear shear behaviour of anchors is represented by NLLink elements. It is concluded that, suggested anchor shear model may be used for modelling external shear wall anchor behaviour.

© 2015 MIM Research Group. All rights reserved.

Keywords: External shear wall Chemical anchor Shear strength Anchor shear model Nonlinear analyses

1. Introduction

Most of the existing reinforced concrete residential buildings in many countries are seismically deficient because the load carrying system of these buildings contains deficiencies like soft stories, nonseismic reinforcement detailing and strong beam-weak column connections [1]. Safety and prevention of total collapse of a structure are the prime requirements of buildings. In order to meet these requirements, the structure should have adequate lateral strength, lateral stiffness and sufficient ductility [2]. Heavy damage and total collapse of RC buildings after the major earthquakes in the last three decades has initiated studies on strengthening techniques [3]. In strengthening reinforced concrete structures, two rehabilitation approaches are generally considered. One is global modification, the other is local modification. In local modification, deformation capacities of components are increased to the determined limit values, so damage occurrence is delayed. But, in this approach, there is no meaningful change in lateral load capacity. Adding concrete, steel, FRP (Fiber Reinforced Polymer) and reinforced concrete jackets for columns are possible methods for this approach [4]. In global modification, a general

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modification is aimed. Reinforced concrete or steel shear walls are added. In Fig. 1, the effect of these two strengthening approaches on lateral load and deformation capacity are illustrated.

(a) (b)

Fig. 1 Comparison of component (a) and system (b) strengthening [4]

In local modification, ductilities of components are usually increased for contributing ductility of the structural system. In global modification, load capacity of the structural system is increased by increasing the strength and stiffness of the structural system. In this way, structural system can fulfil the seismic forces with enough safety.

In global modification, adding shear walls is usually preferred. If addition of the shear wall is inside the structure, reinforced concrete shear wall is placed by removing existing infill wall. If the addition is outside of the building, shear wall can be added without removing existing infills. By rehabilitation of existing infills, the lateral load capacity of structure can be increased, as well. Research on this subject is in progress [1].

Recently, it is observed that lateral stiffness and strength of damaged and non-damaged reinforced concrete frames can be increased considerably by strengthening infill walls [5]. Besides, it was stated that infill walls can be used to control inter-story drift and out-of-plane failure [6].

It is concluded that, external shear wall application can provide system rehabilitation effectively and economically. Thus, in recent years this method is used commonly. Chemical anchors are widely used in external shear wall applications [7]. However, it is known that shear behaviour of anchors have an impact on capacity. Though, it is noticed that there is not any model concerning shear behaviour of anchors. In the referenced study [8], a model is suggested for shear behaviour of anchors by using multiple regression analysis. In this study, this shear model is used with the aim of modelling behaviour of external shear walls and compared with experimental results.

2. Material and Method

Chemical anchors are widely used to connect structural elements. They are embedded in the holes placed in hardened concrete. The diameter of the anchor hole which is drilled is at most 50% larger than that of the bar diameter. Chemical anchors have begun to be frequently used with the development of high resistance adhesives.

In the existing literature, it is observed that there are limited studies about shear behaviour of anchors. Besides that, there is not any model suggested for shear behaviour. In this study, two-story, one-bay RC frame specimens strengthened with external shear walls are modelled in SAP 2000 [9] and nonlinear static pushover analyses are performed. In analyses, anchor shear model established by using multiple regression method is used to


55

simulate shear behaviour of anchors [8]. Nonlinear static pushover analyses can be described as pushing until the stability of the structural system is lost. The applied lateral forces should represent behaviour of structure under lateral earthquake forces. The representative lateral load pattern is simultaneous lateral loading in experiments as pushing from floor levels. Scale of force between 1st and 2nd floor is considered as 1:2 (Fig. 2).

Fig. 2 Load pattern used in analyses

After determining load pattern, by controlling displacement of the roof or a certain node, lateral forces are applied monotonically step-by-step. In every step, relationship between the base shear force and the displacement of the roof is recorded. Also, it is controlled that, if predetermined hinge zones are reached their capacity. In plastic hinge zones, structural component is divided into two and hinge zone is transformed to a node. A rotation redor is defined for this node that represents rotation stiffness and analysis goes on. Analysis continues until the structure loses its stability. Thus, capacity curve (lateral load-roof displacement) is obtained (Fig. 3). In this study, multi pointed idealization is conducted with NLLink elements (nonlinear connection) rather than classic plastic hinges.

Fig. 3 Load pattern and base shear-roof displacement [10]

Suggested anchor shear model (Eqn.1) represents the shear behaviour of anchors that connect external shear wall and existing frames (Fig. 4).

Vt

Vt

Vt

Vt


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Fig. 4 Frame strengthened with external shear wall

0.50.5y

fa L55.3)FL(D2D)(L44.10V c (1)

Here, Va: Anchor shear load (kN); fc: Concrete compressive strength (kN/mm2); fy: Steel yielding strength (kN/mm2); D: Steel diameter (mm); L: Embedment depth (mm).

In this equation, anchor shear value is dependent on anchor diameter (D), embedment depth (L), compressive strength of concrete (fc) and steel yield strength (fy). In Fig. 5, parameters of suggested anchor shear model formula are given.

Fig. 5 Some parameters of suggested anchor shear model formula.

Nonlinear load-displacement features are calculated by using suggested model for anchors having different diameter (D) and embedment depth (L) as given in Table 1. For all anchors, embedment depth (L) is 10. Namely, for 6, embedment depth is 60 mm, for 8, 80 mm, for 10, 100 mm. Experimentally determined mean yield strength value is used as yield point of steel. Here, C1, C2, C3 represent the concrete compressive strength of specimens, 5.7 MPa, NLLink element representing the anchor.


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Table1 Suggested model strength at different displacements and for different concrete grades for S420a steel

Displ.

(mm)

Anchor shear load

Va (kN)

6 8 10

C1 C2 C3 C1 C2 C3 C1 C2 C3

0 0 0 0 0 0 0 0 0 0

2 11.52 11.62 11.94 14.63 14.74 15.08 18.96 19.07 19.42

4 8.83 9.04 9.68 12.53 12.76 13.43 17.69 17.92 18.61

6 6.31 6.63 7.59 10.41 10.74 11.76 16.12 16.47 17.51

8 4.06 4.48 5.77 8.49 8.92 10.27 14.62 15.08 16.47

10 2.06 2.59 4.20 6.74 7.29 8.98 13.24 13.81 15.56

12 0.29 0.92 2.85 5.19 5.86 7.88 11.99 12.68 14.78

14 - - 1.69 3.81 4.58 6.94 10.88 11.69 14.13

16 - - 0.71 2.57 3.46 6.16 9.89 10.81 13.61

18 - - - 1.49 2.48 5.51 9.02 10.05 13.20

20 - - - 0.51 1.61 4.99 8.25 9.40 12.90

22 - - - - 0.86 4.57 7.59 8.85 12.69

24 - - - - - - - 4.26 12.58

In Fig. 6, comparison of shear capacities of anchors by suggested shear model and ACI 318 [11] formulation are given for all anchor experiments.

Suggested anchor shear model is established with the results obtained from the tests of the anchors distant from the edges. Thereby, all of the anchors reached their capacity with steel damage. However, if the anchor is close to an edge, there may be critical changes in anchor behaviour. Suggested anchor model may lead to errors if the anchors are close to the edges. For this reason, it is suggested that more accurate results may be get for the anchors that reaches ultimate capacity by concrete failure by reducing the strength values by Eqn. 1 with respect to the ACI 318 [11].

In ACI 318 [11], three collapse modes are identified. These are concrete pryout failure, concrete breakout failure and steel failure (Fig. 7).

Steel failure can be determined with Eqn. 2:

utafseAn6.0saV (2)


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Fig. 6 Comparison of shear capacities of anchors by suggested shear model and ACI 318 [11] formulation

Fig. 7 Anchor failure modes under shear loading in ACI 318 [11]

Here, n is number of anchors in group, Ase is cross sectional area of an anchor (mm2), utaf

is, tensile strength of the anchor steel (N/mm2).

In concrete edge failure, breakout capacity for single anchor ( bV ) can be computed by Eqn.

3.

5.11a

'c0

2.0

0

eb )c(fd)

d

l(6.0V (3)

Here, el (mm) is effective anchor depth, 0d (mm) is bar diameter , 1ac (mm) is distance to

free edge taken in the direction of the applied shear and '

cf (MPa) is specified concrete

strength. For the pryout collapse of concrete, ACI 318 [11] presents Eqn. 4 and Eqn. 5 for single and group anchors respectively.

cbcpcp NkV (for single anchors) (4)

cbgcpcpg NkV (for group anchors) (5)

a) concrete pryout failure b) concrete breakout failure c) steel failure


59

Here, cpV (N) and cpgV (N) are nominal concrete pryout strength of single and group

anchors; cbN (N) and cbgN (N) are nominal concrete breakout strength in tension of single

and group anchors, respectively. cpk is a constant that changes with embedment depth of

anchors. For shallow anchors (hef <65 mm), cpk is 1.0. For other effective depth values (hef

≥65), cpk is 2.0.

In ACI 318 [11], no relation between anchor displacement and corresponding strength is given. As all the tests used to develop the given model contain anchor far from edges, ACI 318 strength values are used as an upper bound for the obtained strength values. However, please note that the displacement-strength relationship is still used as suggested by the proposed model. Fig. 8 illustrates the modification for the anchors that may reach capacity by concrete failure.

Fig. 8 Modification for the anchors that are close to edges using ACI 318 strenght as upper bound

Lateral load-displacement relationship related with NLLink components are as given in Figs. 9-11 for different anchor diameters and concrete types. Strengths obtained according to suggested model and reduced values of these strengths which are obtained by using formulas in ACI 318 [11] as an upper bound.

Fig. 9 Properties of NLLink components modelling6 anchors


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Fig. 10 Properties of NLLink components modelling 8 anchors

Fig. 11 Properties of NLLink components modelling10 anchors

Using suggested methodology, shear strength of anchors, which are modelled with NLLink components, are determined with respect to the displacement level. Established NLLink components can also carry load outside of given displacement limits. Load values outside of given displacement limits are determined by continuing last slope line. For that reason, a permanent force value in NLLink components are formed outside of displacement limits reflecting the residual capacity. This zone can be seen as constant force zone in the end of graphics.

3. Features of external shear wall

In the experiments of external shear wall, it was observed that TS500 [12] formula can provide a certain safety coefficient in anchor components with a small diameter. By using anchor shear forces determined with this way, sixteen specimens are tested under repetitive and reversible loads. Specimens are produced with three different types of concretes, C1, C2, C3 as explained above. Connection with external shear wall and existing frame is provided with anchors that are embedded to the columns and beams of these specimens. For representing the deficiencies of the structures in Turkey, the specimens are produced with low compressive strength concrete.

Anchors in connections of shear wall and columns and beams in the specimens are varied. The cases are named as C1, C2 and C3 according to concrete strength of frames and beam-traverse anchor ratios. These frames are strengthened with shear walls with concrete compressive strength of 30 MPa.

In Fig. 12, two- story, one-bay RC frame dimensions; in Fig. 13, steel detailing of columns and beams are given. Anchorage amounts which were used in frame tests of reference study can be seen in Table 2.


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Fig. 12 Dimensions of two- story, one-bay RC frame specimens

Fig. 13 Detailing of columns and beams


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Table 2 Anchorages used in frames retrofitted with outer shear wall

Test Frame Models

1st Floor

Column

2nd Floor

Column

1st Floor

Beam

2nd Floor

Beam

C1DE 36+28 16+28 18 36

C2ED 16+28 36 26 16+28

C2AA 410+28+36 26+58 38+16 78

C2BA 310+18+26 110+38 110+36 68+26

C2BB 58+36 48+16 28+16 210+18+26

C2DA+ 110+28 28 410+28+16 410+28+16

C3HD - - 26 16+28

C3DH 36+28 16+28 - -

C3DG 16+28 36+28 16 18

C3EE 16+28 36 18 36

C3AA 410+28+36 26+58 38+16 310+46

C3BA 310+28 210+26 38+16 310+46

C3BB 210+48+16 28+46 110+26 48+26

C3BB+ 310+18+26 110+38 28+16 510+28

C3DA+ 18+46 18+26 410+28+16 110+18+26

C3DD 36+28 16+28 26 16+28

4. Non Linear Analyses of Strengthened Frames

Two-story, one-bay RC frame specimens tested in [13] and [14] are modelled using SAP 2000 [9]. Behaviour of anchors connecting the frame and shear wall is reflected with NLLink elements using proposed model Nonlinear pushover analyses are performed. Capacity curves which was derived from analyses and envelope curves which was derived from test data is given in Figs. 17-18.

4.1 Structural Model Info Performed Using SAP 2000 [9] Software

For composing structural analyses, two dimensional models of test frames, as seen in Fig. 14, established in SAP 2000 [9] software. In these models, nonlinear behaviour that can be occur in shear walls, columns, beams and anchors were considered. Nonlinear pushover capacity curves obtained from analyses were compared with experimental values. In SAP 2000 [9] models, experimental values for material strengths for shear walls, columns, beams were used.


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Fig. 14 Hinges and NL Links in SAP 2000 [9] models

Frame and shear wall were modelled side by side as given in Fig. 14. Infinitely rigid beams are connected to the shear wall in story levels. In this way, wide column analogy is considered for modelling of the shear wall behaviour. As it can be seen in Fig. 15, in wide column analogy, shear walls can be modelled as a column that is located at the axis of the shear wall. Through the B dimension of the shear wall, infinite flexural stiffness is considered (EI=∞) [15]. Wide column analogy is therefore a tool which is not only available to researchers but also to design engineers [16].

Fig. 15 Using wide-column analogy in modelling of a shear wall-frame system

Connections between shear wall and frame beams in story levels were provided by lateral NLLink components. Shear force-displacement behaviour of all anchorages between the shear wall and a story beam was provided by a single NLLink component. Load transfer of RC shear wall and columns were provided using NLLink components from the midpoint of the story levels. In the model, EQUAL components were assigned for providing rigidity between endpoints of NLLinks and RC shear walls.


64

EQUAL constraint makes sure that the located place in the chosen degree of freedom moves with same amount of displacement. A, B, C and D points define the mid points of the story levels. These points displace along with A’, B’, C’, D’, owing to EQUAL constraint.

Hinges were defined at the endpoints of beams and columns. Flexural capacity of shear wall component was calculated and is considered in nonlinear model. For representing hinging in the endpoint of shear wall, NLLink components were used. Moment-curvature relationship belonging to shear wall was obtained by using SEMAp [17] software which was developed for modelling nonlinear behaviour of reinforced concrete components.

Moment–rotation behaviour of external shear wall was modelled with an idealization as given in Fig. 16. Obtained moment-curvature relationship was transformed into moment–rotation behaviour. Elastic rotation during yielding and plastic rotation in hinge can be calculated respectively with Eqn.6 and Eqn 7.

(6)

(7)

In these equations, is yielding rotation; is yielding curvature; is rotation

capacity of plastic hinge, is the ultimate curvature, is size of plastic hinge.

Fig. 16 Moment-rotation relationship which was calculated for shear wall component

In columns located on endpoint of shear walls, besides anchor damage, columns can fail under axial load and rupture of steel reinforcement by tensile forces is possible. For that reason, compressive and tensile strength capacities of columns were considered in nonlinear model.

4.2 Comparison of Experiment and Analyses Results

The suggested model and reduced values with ACI 318 [11] formulation for SAP2000 [9] results are given for comparison with experimental values in Figs. 17-18. Modified model with ACI 318 [11] capacity values, have lower capacity due to reductions made for possible concrete failure. An amount of decrease in capacity was observed in all models after reaching lateral load capacity. This decrease indicates that capacity of anchors have started

pyy

pyup )(

y y p

u p


65

to decrease. In Figs. 17-18, the continuous line named as “Monolithic Behaviour” represents the case of shear wall with full capacity reflecting the monolithic behaviour with the frame. The reduction in capacity due to connection with anchors is obvious in figures. The red dotted lines in the figures represent the suggested model modified for concrete failure using ACI 318 strength values as upper bound.

Fig. 17 Envelope curves of C1 and C2 test specimens and capacity curves of SAP 2000 [9]

Differences in lateral load-displacement curves which were obtained as a result of experiments and analytical studies can be related with applied cyclic load during experiments. In the analyses, the mentioned load pattern is applied in a monotonically increasing manner and the rigidity loss is not directly taken into account.

Maximum load and collapse damages obtained in SAP 2000 [9] models for all of the frames, strengthened with external shear wall, are seen in Figs. 19-30. The black dots represent heavy damage and failure at the corresponding points.


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Fig. 18 Envelope curves of C3 test specimens and capacity curves of SAP 2000 [9]


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Fig. 19 Maximum load and component damages in case of collapsing for C1DE model

Fig. 20 Maximum load and component damages in case of collapsing for C2ED model

Fig. 21 Maximum load and component damages in case of collapsing for C2AA model

Fig. 22 Maximum load and component damages in case of collapsing for C2BA model


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Fig. 23 Maximum load and component damages in case of collapsing for C2BB model

Fig. 24 Maximum load and component damages in case of collapsing for C2DA+ model

Fig. 25 Maximum load and component damages in case of collapsing for C3HD model

Fig. 26 Maximum load and component damages in case of collapsing for C3DH model

Fig. 27 Maximum load and component damages in case of collapsing for C3DG model


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Fig. 28 Maximum load and component damages in case of collapsing for C3EE model

Fig. 29 Maximum load and component damages in case of collapsing for C3AA model

Fig. 30 Maximum load and component damages in case of collapsing for C3BA model

5. Results and Discussion

In this study, finite element models of two-story, one-bay RC frame specimens strengthened with external shear walls in Pamukkale University Earthquake and Construction Technology Research Laboratory were performed using SAP 2000 [9] software. In these models; nonlinear behaviour of anchors connecting RC shear wall and existing frame is represented with suggested anchor shear model. Reliability of suggested anchor shear model was tested upon these models. It is observed that, experiment results and nonlinear static pushover results are in consistence. As a result of these comparisons, suggested anchor shear model may be used for modelling shear behaviour of anchors.

Authors emphasize that, in developing process of this model, experimental data of anchors which are sufficiently away from edge were used. But there may be some cases that, anchors embedded close to the free edges, defected concrete existence in the place where the anchors are embedded or anchors reach breakout or pryout failure capacity. All of these factors were considered and lateral load-displacement capacities obtained by using suggested anchor shear model were bounded by the ultimate loads obtained from the formulas in ACI 318 [11].

In case of a compressive strength higher than 20 MPa and with reasonable amount of anchors, it was seen that suggested model and single diecast shear wall are closer compared to others. But, in case of a compressive strength under 20 MPa, capacities obtained by considering both cases were nearly the half of single diecast shear wall.


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Therefore, anchors reach their capacity with steel damage due to the increase of concrete compressive strength. Also, it can be stated that concrete compressive strength of existing structure is very important when calculating shear capacity. In specimens, the least value for concrete compressive strength is 5 MPa. Thus, use of this model in structures that has concrete compressive strength under 5MPa is not suggested because it is not in scope of the study.

Acknowledgements

This study has been supported by the Turkish Scientific Resesarch Council (TÜBİTAK) through Project No. 107M572 and Suleyman Demirel University (SDU) through Project No. 1458-D-07, BAP. Authors sincerely thank TÜBİTAK and SDU for their contributions. Additionally, authors are grateful to the staff of Pamukkale University Earthquake and Construction Technology Research Laboratory due to their contributions in the experimental study.

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A model for shear behavior of anchors in external shear